“The measures are expected to help tens of thousands of families and businesses, making it easier for them to build extensions,” No 10 said, adding that more conservatories and extensions would provide “a crucial and immediate stimulus to the construction sector.

But in a BBC interview, Mr Boles said he did not know how many people would take advantage of the new rules, and suggested the Government had no formal estimates of the effect of the policy.

He said: “I don’t know and you’d be a bit of a fool to be able to project precisely. Do you know the number of people who want to build a conservatory or extend their house? That would be quite a difficult number to guess.”

Critics of the conservatories plan have suggested that it will do little to address the fundamental problems of the housing market, which

The minister, appointed in this week’s reshuffle, insisted that the changes will have some sort of positive impact.

“What is clear is that it is important to make it easier for people to do it, and to encourage people to do it now, rather than wait for three years time when they’ll have to go through the planning process,” he said.

Domestic planning application fees are typically £150, and paying professional advisors can cost thousands more. Applications can drag on for months, although around 90 per cent of are eventually approved.

“People want to do these things, they do apply for planning permission, but it’s a painful and expensive process, and if you make it less painful and less expensive, more people will want to do it,” Mr Boles said.

Mr Boles, a political ally of Mr Cameron, has previously made disparaging remarks about rural campaigners who opposed weakening protections for greenfield land.

In the interview, his first since taking up his post, the minister repeatedly refused to rule out any changes to legislation on the green belt in the coming weeks.

No changes in green belt rules have been announced this week, but next month, ministers are expected to publish an Economic Development Bill that could propose changes.

George Osborne, the chancellor, has said he wants to accelerate the planning approval process for housing projects and other major developments. That will mean cutting time limits for appeals and making it harder for those who object to win a judicial review of planning decisions.

He has also encouraged councils to make greater use of existing rules that allow them to permit building on green belt land. Some ministers are pressing for those rules to be strengthened in the new legislation